Final answer:
The work done on a 4 kg object accelerating from 3 m/s to 6 m/s in 8 s is 54 J, which is the change in kinetic energy. None of the provided multiple-choice options matches this answer, implying a potential error in the question or the options given.
Step-by-step explanation:
To find the work done on the object, we should use the work-energy theorem which states that the work done on an object is equal to the change in its kinetic energy. The kinetics energy (KE) is given by the formula KE = 1/2 mv² where m is the mass and v is the velocity. Since the object's mass is 4 kg and its velocity changes from 3 m/s to 6 m/s, we first find the initial kinetic energy (KEi) and the final kinetic energy (KEf) using the given velocities.
KEi = 1/2 × 4 kg × (3 m/s)² = 1/2 × 4 × 9 = 18 J
KEf = 1/2 × 4 kg × (6 m/s)² = 1/2 × 4 × 36 = 72 J
The work done on the object (W) is the change in kinetic energy, so:
W = KEf - KEi = 72 J - 18 J = 54 J
However, since 54 J is not one of the multiple-choice options provided, and if we consider that there might be a typo in the question, we can still decide which of the given options is closest to the correct answer. The closest option to 54 J is "b) 36 J." Therefore, there might be an error in the question provided by the student or in the choices given.